# Solution: Random Pick with Weight

Let's solve the Random Pick with Weight problem using the Modified Binary Search pattern.

We'll cover the following

## Statement

Youâ€™re given an array of positive integers, weights, where weights[i] is the weight of the $i^{th}$ index.

Write a function, Pick Index(), which performs weighted random selection to return an index from the weights array. The larger the value of weights[i], the heavier the weight is, and the higher the chances of its index being picked.

Suppose that the array consists of the weights $[12, 84, 35]$. In this case, the probabilities of picking the indexes will be as follows:

• Index 0: $12/(12 + 84 + 35) = 9.2\%$

• Index 1: $84/(12 + 84 + 35) = 64.1\%$

• Index 2: $35/(12 + 84 + 35) = 26.7\%$

Constraints:

• $1 \leq$ weights.length $\leq 10^4$

• $1 \leq$ weights[i] $\leq 10^5$

• Pick Index() will be called at most $10^4$ times.

Note: Since weâ€™re randomly choosing from the options, there is no guarantee that in any specific run of the program, any of the elements will be selected with the exact expected frequency.

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